1

Sci.Rep.Fukushima Univ.,No.33(1983)

Single-Meson Inclusive Cross Sectionsand Sequential Decay of Reggeons

ToshihiroYosHIDA

Department of Physics Factdty of E:ducatt°on. Fukushima Uni11e「SityFttkttshima 960-12

(Recezがed 10 September 1983)

15

The sequential_decay mechanism of Reggeons with the hypothesis Of tWo-ReggeOn fma1states Is applied to the single-particle inclusive cross sections of mesons P「educed f「Om Incident mesons Data on f[二and K:': production from ?'or K'in the 「egiOn .x>0With t)T =03and05Gev/c at 100 and 175GeV/c are analysed. It is shown that the many- particle production effect and the initial-decay effect give rise to Components P「Ope「tiOna1 to (1_x)3and 1-,てrespectively.

l. Introduction

The hypothesis of two_Reggeon fma1 states has been applied to analysis Of had「On reactions:This leads to the two-component structure of Pome「On in the total C「OSS Sec- tions,1 The energy dependence of the single-particle inclusive cross sections in the ta「get fragmentation region is successfully explained with the hypothesis.21 The Sequential-decay mechanism assumed for Reggeons,together with the hypothesis,leads to the fact that the multiple_production cross sections consist of the components due to the many-Pa「flote production effect and the initial-decay effect.31

The Feynmannx dependence of the single-meson inclusive cross sections in the ta「get- proton fragmentation region has been investigated.41 The components due to the many- particle production effect and the initial-decay effect show the POWe「-law behaViOu「S(1-X)5 and (1_x)3 respectively The behaviours are consistent with Gunion'S Spectate「 Counting rule based on QcD diagram;51 the process p→π一,for which a special t「eatment Was neces- sary in the rule,is explained without artifice in cur scheme.

In this paper we study the many_particle production effect and the initial-decay effect in the single_particle inclusive cross sections of mesons produced from incident mesons・ The paper ls organized as follows: In the next section contributions of the effects to the C「OSS sections are investigated. In the following section data at 100 and175GeV/c ot incident momenta61 are analysed for transverse momenta t,T=0.3 and 0.5 GeV/c. Components proportional to (1_1c)3and1_x are obtained as the many-particle production effect and the Initial_decay effect,respectively. Discussion is carried out in the final Section・

2

16 T.YOShida:Single-Meson Inclusive Cross Sections and Sequential Decay of Reggeons

Table I Mesonic Reggeons formed in the hadron_hadron to Reggeon-Reggeon processes 01 f,-p and K p scatterings

D s b 1

1.iid ] [14dl X2, [ad],f ia4]

[alti] [d'tit X2,[dd],[-uu] 1us] [us],?_ds][su] [su],.[sd]

t ;d][ s u ]

[1liu],.[ud],[ss]

al Htypeand X type without strangeness exchangebl H type andX type with strangeness exchange.

2. The many-particle production and initial-decay ef fects

In hadron reactions,the initial hadrons form a Reggeon each;and the Reggeons decay into hadrons which appear in the final states. The quark contents of mesonic Reggeons fo「med in the hadron-hadron toReggeon-Reggeon processes of 1) Handx types areljsted in Table I for lr かand K'1)scatterings;71 here S means H andx types with strangeness exchange,whereas ff is for those without strangeness exchange

The mesonic Reggeons formed in the hadron-hadron toReggeon_Reggeon processes can decay into mesons in the final states by the sequential decayof je states,31 where a j estate Can decay into two (1(1 states connected to the initial state and each other by quark lines The ffeStates being numbered as given in Table Ila,the relative probability with which the 1-th State iS found among the states produced from the J_th state is given by the (j,J)

Table IIa.The(jq states

uu 11S、 dS su sd

Table lib. The elements of 2(2十,)Y

2110-0

00

1201(と00(と0

10210,(00

01120(0--0

・

1100十100(-

1 t「-

00111十00(-

一J

l

101000十1一と

1 -

0101001十g

1

000011112-

3

Sci.Rep.Fukushima Univ.,No.33(1983) 17

element of the matrix Y shown in Table jib,where the creation probability Of St「ange-qua「k pairs Is assumed less by the factor ε. The production probability in the n-Step Sequential decay is proportional to the element of Yn。 It can be shown that

Y = Y l °1-'r Y 'n 1,

(Y 1°1).J = __1= a _ _e ,, (Y l'1),,= a nY ,J, (2 ・ 1)(2十i )

with e,= e2=:二e3= e4=二1,e5= e6= e7= e8= ?,e9= ?2 and ar,= 2-「-';Yil t iS into「P「eted as the many_particle production effect,while Yl'11s the initial-decay effect.

The single_meson inclusive cross sections include contributions of all steps consistent with the energy and momentum conservation. The result is that the cross sections fo「 a十P →(、十X is written as

(:1(a , c )=:c;o(a , c )十(;,(a , c )十(;,(a , c )十(fo(a , c )十(; (a , c )_ (2 ' 2 )

Here the components lie and(j ,which are due to the many-particle production effect and the initia]-decay effect,are given by

(:1k(a,(:)_ ∑R3(ac)[∑Ak(n)GnlFQ,0 n

Ao(?1)= -j-二j , A,(n)=::2-(-2? -g-), (2 3)( 十 c ε

whereFomeans the weight associated with contributions o[Q type(Q=D,H S),and Gn Is a factor for the weight of the contribution of then-step sequential decay. The leading-

Table m. The coefficients R'ら(ac),ito(ac)and ?ら(ac)

RS

011

1 十i

3? 1 十? 2 十c; 1十21

3E: 0 0 1十i 0 0 0 0 0 1十?2十(_ 0

3-k0o

1一32一31一3:2-3

・一32一31-32-3

0

2一い

0

2手

0

2手

0

2一い

222-3・〇一311-一35一30k0・on

1一3-一30

2一3

2一34-30

0

4

18 T.Yoshida:Single-Meson Inclusive Cross Sections and Sequential Decay of Reggeons

particle effect due tothemesonsthat come fromthemesonic Reggeonswithout the sequential decay is given by

(ff,(a ,c )= ∑ li e(ac )GoFo (2 ・4)e D ,H

The components (;?and (f are due to the mesons produced from the baryonic Reggeons formed from the target proton and given by the similar expression as Eq.(2・3)with coefficients ?3(ac)_3' The coefficients RQ s for a,c=二??or K-are given in Table m.

Let us decompose σ's into ingredients A's as(:1(a-,c-)= A,(ac)十Ao(ac)十A,(ac), (2 ・5a)(f(a-,c')= Ao(ac)十Ap(ac ), (2 ・5b)c1(a-',c-)= Ao(ac ), (2・5c)c;(a',c')= A,(ac)十Ao(ac)十A,(ac)-?Ap(ac). (2 ・5d )

Under the assumption that the contribution of S type and the initial-decay effect of mesons from baryonic Reggeons of ff type are negligible,we have

Ap(ac )= Ap(ac ), ac = .??,K71: frK ,K K ; (2 ・6)the case ac= frr holds without the assumption and the case ac=Kt[holds with only the assumption of negligible S type. We also have

Ap(?? )= Ap(K?)= Pt , (2 ・7a)Ap(IrK )= Ap(KK )= 2gF,j, (2 ・7b)

where P,)indicates the initial-decay effect of mesons from the baryonic Reggeons with D type.

At very high energies,because the contributionof j type dominates others,in addition to (2・7)we have

Ao(- ?)- Ap(?? )= Ao(Kit )- Ap(Kit )= D° (2 ・8a)Ao(?K )= Ao(KK )= E,1)', (2 ・8b)

;A,(- = At(Kt[)= .D , (2・9a)A,(IrK )= eD', A,(KK )= (]十e)D', (2 ・9b)

where .D?means the many-particle production effect (from not only mesonic but also baryonic Reggeons),while D is for the initial-decay effect from mesonic Reggeons.

3. Analysis of data at PT=0.3and0.5GeV/c

Data on (f(a-,c-),(f(a-,c )and ?i(a+,c-)with a,c=? or K are available to obtain the behaviour of the ingredients A's at 100 and 175GeV/c with PT=03and 0.5GeV/c 61 Figures l and2 show the x dependenceof Ao(m-)- Ap(m・),Ao(Kilt)-Ap(Kfr)and Ao(rK) The least-square fits toC(1一ス1)3 given by solid lines fit well except for x>05at 100GeV/c. The parts which deviate from (1-x)3 behaviour are fitted well by C(1-)c)as shown by dotted lines in the figure. The ,?dependence of A,(??)十A,(π?),A,(K?)and A,(rK)are shown in Figs.3 and4;the least-square fits to e(1-x)are given by the solid lines_

Together with Eqs.(2・8)and (2・9),the values C obtained in the least-square fits, which are given in Table Iva and IVb,estimate the factor E;the results are shown in Fig_ 5.Their average isE=0.14_

5

Sci.Rep.Fukushima Univ.No.33(1983) 19

Fig 1 A.(- _ Ap(- ,Ao(K?)_ Ap(K.1r)and Ao(IrK)in rub/(GeV2/c3)at 100GeV/C:(a)1:,r=G3Gev /c,(b)I T=05GeV/c. From the top to the bottom,π?,K五and flK a「egiven The cases Kπ(j Kl are multiplied by1/10(1/100);they are displaced to the 「ighta little,the position of ?=0 being denotoed by the dashed-dotted(dashed-dotted-dotted)lines near and para11el totheordjnates. The solid lines indicate theleaSt-Squa「e fits toc(1_ t.)3,while the dotted lines are those to C(1-z). The abscissae are P「Ope「tiOnaito log(1- r ).

6

20 T,Yoshidal Single-Meson Inclusive Cross Sections and Sequential Decay of Reggeons

C

一

)

Fig.2_ A・(m'1- Ap(m,),Ao(Kft)- Ap(K7[)and A.(?K )in rub/(GeV2/c3)af t75GeV/c :(a)fi'T=0。3GeV/c;(b)?r=0.5GeV/c. From the top to the bottom,1rr,K? and ltK aregiven。 The cases Kit(1tK)are multipliedby1/10(1/100);they aredisplacedtothe righta little,the position of ?=0 being denoted by the dashed-dotted(dashed_dotted dotted)lines near and para11el totheordinates. The solid lines indicate the least_square fits toC(1-x)3. The abscissae are proportional to log(1-x;).

7

Fig.3

C一

,58 _ .,9 _ . ,68 - ・、/ 、

(at (b)

A,(m )十At(M ),A,(K7,)and A,(rK )in rub/(GeV2/c3)at100GeV/c :(a)?T=0_3GeV/ (b)fir=05Gev/c From the top to the bottom, ??,Kit and ?K are given. The casesKlr(frK)are multjpljedby1/10(1/100);they are displaced to the right a little,the posltlon oj x=0 being denoted by the dashed-dotted (dashed-dotted-dotted)lines nea「 and para11el tothe ordjnates. The solid lines indicate the least-Squa「e fits to e(1-「)。 The abscissae are proportional to jog(1-x).

21 Sci.Rep.Fukushima Univ.,No.33(1983)

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22 T.Yo、shida:Single-Meson Inclusive Cross Sections and Sequential Decay of Reggeons

Fig_4

:;t )? 4 っしi U . 。 6 8 4 ,) 9X x(a) (b)

A,.(1tlr)十A (??),A,(K?)and A,(IrK ) in rub/(GeV2/c3) af t75GeV/c :(a)1)r=03GeV/c,(bl tiT=05GeV/c_ From the top to the bottomf ??,K? and ltK are given.The Cases K定(KK)aremultipiiedby1/10(1/100);they are displaced to the right a little,the position of x=0 being denoted by the dashed-dotted (dashed_dotted_dotted)linesnea「 and Para11el to theordinates. The solid lines indicate the least_square fits toC(1-.?). The abscissae are proporitional to1og(1_z)_

9

Sci.Rep、Fukushima Univ.,No.33(1983)

Table Iva The values C obtained in the least-square fits toC(1 - x )3 for Acl frft)- A p(,7,? ),A o(K 7t)- A f'(K ? ) andA o ( ・,,K )

23

PT=

100GeV/c0.3 0.5

175GeV/c0.3 0.5

9.05::l二0.58 7.31±1.81 1_47±0.08

3.75:十0.40 2_48±1.70 0.64±0.12

9.94::l二0.57 9.00±1.82 1.04±0.12

4.79十0.39 5.26十1.21 095±0.10

Table Ivb.The values C obtained in the least-square fits toC(1-x)for A,(K7r)and A,(7,K)

PT=

100GeV/c0_3 0.5

175GeV/c0.3 0.5

2.19±0.28 0 28十0.03

1.11士0.41 0.20十0.04

2_25±0.46 0.40±0.05

0.89::l二0.18 0.13-1-0.03

Fig 5 The factor i estimated from Eqs.(2・8)and (2・9):The white(black)circles are those calculated from一;1K.・l and 1てK in Table Iva and the triangles arethose from K;r and ;rK in Table IVb_ The dottedlines show the weighted averages.

Discussion

Figures 1_4 show that the components due to the many-particle production effect and the initial_decay effect have the power-law behaviours C(1-)c)3 and C(1-,x), 「eSPeCtiVely・ Though the fits are not the best ones among the least-square fits to e(1-1;)''With intege「n In all cases,the fits with f1=3or l are generally in good agreement with the Components derived from the data.

The deviation of 40(?? )_ 4p(7,,),Ao(K7?)- 4p(K? )and 40(7[K )f「Om the POWe「-law

behaviour (1_t.)3jn the region with the larger ). at 100GeV/c can be att「ibuted to the contribution from the initial_decay effect with H type. This contribution iS expected to be In proportion with 1_1;in the same manner as that with D type and to become Smalto「 as the

10

24 T.Yoshida:Single-Meson Inclusive Cross Sections and Sequential Decay of Reggeons

energy increases;this is in agreement with the fact that the deviation is not clear (because it is small enough)af t75GeV/( in contrast with at 100GeV/(、(as well as the power_law behaviour).

Therefore we can conclude that the many-particle production effect gives rise to Components proportional to (1-,1-)3 and that the initial-decay effect results in components proportional to 1-.?_ The exponents n_2in the least-square fits toe(1-t) obtained for K- →fr''and i '→K-61 are attributed to the existence of the many-particle production as well as initial-decay effects in the processes.

The ingredients Ap(a()obtained from the data do not show clear behaviour,unlike the others. As the ingredients come fromenty the initial-decay effect of mesons produced from the baryonic Reggeons formed from target proton(even with inclusionof ff type but not of S type),they are expected to decrease rapidly as.zincreases;some of them show such large decreases,especially in the smaller 文,region。

Acknowledgement

The computer calculation for this work has been financially supported in part by Institute for Nuclear Study,University of Tokyo. The author would like to express his gratitude to the staffs of Computation Centre,Fukushima University,where the main part of the numerical calculation was peorformed. He is also indebted to Computer Centre,Tohoku University,where the drawings were prepared。

He thanks toDr.M.Pidoux for the reading the manuscript.

References

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(1982),21_4 ) T _ Y OS h i d a , R ( (. (?;It P r o g r (:s s i ,1 f )?,o d 1?? 110 )I M , (、11m i s m s 111 l f l g 11 f n e r g y (:、o f l j s 1o ,1、s ( f f

、ii(、l ei川s m ?f .、if(、l e i (R I FP -465,Kyoto U ni v., 1981),p.42.

5) J.F.Gunion Phys.Lett.88B(1979),l50.6) A.E.Brenner,D.C.Carey,J_E.Elias,P.H.Garbincius,G.Mikenberg,VA.Polychronakos,w.Aitken_

head,D.S.Barton,G.W.Brandenburg,W.Busza,T.Dobrowolski,J.I.Friedman,H.W.Kendal1,TLyons B.Nelson,L.Rosenson,W.Toy R.Verdier,L.Votta,M.T.Chiaradia,C.DeMarzo,CFavuz_ZI G。Germinario,L_Guerriero,P.LaVopa G.Maggi,F.Posa,G.Selvaggi,P.Spinelli,F.waldner,R.Meunier,D.Cutts,R。S.Dulude,R_E.Lanou,Jr.and J.T_Massimo,Phys.Rev.D26 (1982),1497.

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